The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains

Wood, Ian (2009) The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains. In: Janas, Jan and Kurasov, Pavel and Naboko, Serguei and Laptev, Ari and Stolz, Gunter, eds. Methods of Spectral Analysis in Mathematical Physics. Operator Theory: Advances and Applications, 186 . Birkhaeuser, Basel, pp. 415-435. ISBN 9783764387549. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1007/978-3-7643-8755-6_21

Abstract

We consider bounded Lipschitz domains Ω in ℝ n . It is shown that the Dirichlet-Laplacian generates an analytic C 0-semigroup on L p (Ω) for p in an interval around 2 and that the corresponding Cauchy problem has the maximal L q -regularity property. We then prove that for bounded or exterior Lipschitz domains Ornstein-Uhlenbeck operators A generate C 0-semigroups in the same p-interval. The method, also allows to determine the domain D(A) of A and, if Ω satisfies an outer ball condition, allows to show L p -L q -smoothing properties of the semigroups.

Item Type: Book section
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 09 Apr 2010 10:56
Last Modified: 28 Jul 2014 08:09
Resource URI: https://kar.kent.ac.uk/id/eprint/23941 (The current URI for this page, for reference purposes)
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